Speaker: Maria Victoria Rivas
Complutense University of Madrid

Title: Application of QCRM (Quality Control of Risk Measure) to ORSA
(Own Risk Solvency Assessment)

Abstract:

EIOPA (European Insurance and Occupational Pensions Authority), NAIC
(National Association of Insurance Commissioners), the Office of the
Superintendent of Financial Institutions Canada (OSFI) and other
regulators are working on a new regulatory requirement called ORSA
(Own Risk Solvency Assessment). ORSA is designed to improve the risk
management, reporting and assessment process, especially in the risk
assessment phase. This presentation focuses on the application of Quality Control of Risk Measure (QCRM) to Own Risk Solvency Assessment. QCRM is a
statistical approach to assess the quality of risk measures. The
approach is applied to the problematic of backtesting for the
insurance companies in the framework of ORSA. Finally, we will analyze
the application of the QCRM approach to real insurance data.

 

 

 

 

In the last few years, substantial interest has been given to the study of systemic risk. In this talk we describe a class of models for systemic risk analysis in the setting of insurance and reinsurance participants. The models are constructed with the aim of capturing features such as cascading effects at the time of default due to counter-party risk and contagion. We also impose a probabilistic structure that allows to rigorously study risk analysis questions using the theory of combinatorial optimization. In the end, we are interested in answering questions such as: a) Which group of companies are the most relevant from a systemic risk standpoint?, b) How to quantify the role of reinsurance companies in systemic risk?, c) How to understand and quantify the role of a regulator and associated capital requirements for systemic risk mitigation?

 

This talk is joint work with Yixi Shi.

Speaker: Sheldon Ross, Department of Industrial and Systems Engineering,
University of Southern California

Title: Queueing Loss Models with Heterogeneous Servers and Discriminating
Arrivals

Abstract: We consider an n serve queueing loss model where customer i service times have distribution Fi. Each arriving customer has a vector (X1, . . . ,Xn) where Xi is the indicator of the event that server i is eligible to serve that customer. The vectors of successive arrivals are assumed to be independent with a common distribution. Arriving customers can be assigned to any currently idle server that is eligible to serve the customer; if there are no such servers then the customer is lost. Assuming that the random vector (X1, . . . ,Xn) is exchangeable, we find the optimal policy that minimizes the proportion of customers that are lost both when Fi, 1 i n are exponential with known rates, and, in the case of Poisson arrivals, when the Fi are general but unknown and only idle-time ordering rules are allowed. One such rule would be to assign an arriving customer to a randomly chosen idle-eligible server; another would be to assign to the idle-eligible server that has been idle the longest; a third is to assign to the idle-eligible server that has been
idle the shortest.

 

 

Speaker: Milan Bradonjic, Bell Labs, Alcatel-Lucent

Title: "Bootstrap Percolation on Random Geometric Graphs"

Abstract:
Bootstrap percolation has been used effectively to model phenomena as
diverse as emergence of magnetism in materials, spread of infection,
diffusion of software viruses in computer networks, adoption of new
technologies, and emergence of collective action and cultural fads in
human societies. It is defined on an (arbitrary) network of
 interacting agents whose state is determined by the state of their
neighbors according to a threshold rule. In a typical setting,
bootstrap percolation starts by random and independent ``activation''
of nodes with a fixed probability $p$, followed by a deterministic
process for additional activations based on the density of active
nodes in each neighborhood ($\theta$ activated nodes). Here, we study
bootstrap percolation on random geometric graphs in the regime when
the latter are (almost surely) connected. Random geometric graphs
provide an appropriate model in settings where the neighborhood
structure of each node is determined by geographical distance, as in
wireless ad hoc and sensor networks as well as in contagion. We derive
bounds on the critical thresholds $p_c', p_c''$ such that for all $p >
p''_c(\theta)$ full percolation takes place, whereas for $p <
p'_c(\theta)$ it does not.

Joint work with Iraj Saniee
 

 

 

Hongzhong Zhang, Department of Statistics, Columbia University

Title: Quickest detection in a system with correlated noise

Abstract: The problem of quickest detection arises in many
applications in quality control and financial surveillance. In this  work, we study the quickest detection of signals in a system of 2  sensors coupled by a negatively correlated noise, which receive  continuous sequential observations from the environment. It is assumed  that the signals are time invariant and with equal strength, but that  their onset times may differ from sensor to sensor. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended Lorden's criterion is used as a measure of detection delay, with a constraint on the mean time to the first false alarm. The case in which the sensors employ their own cumulative sum (CUSUM)strategies is considered, and it is proved that the minimum of 2 CUSUMs is asymptotically optimal as the mean time to the first false alarm increases without bound.
Implications of this asymptotic optimality result to the efficiency of the decentralized versus the centralized system of observations are further discussed.
 

 

 

Arian Maleki, Department of Statistics, Columbia University

Title: Phase transitions in compressed sensing

Abstract: Compressed sensing aims to undersample certain
high-dimensional signals yet accurately reconstruct them by exploiting signal structures. Accurate reconstruction is possible when the sparsity of the object to be recovered is below a certain level, a.k.a. phase transition curve. Characterizing the phase transition curve for different reconstruction algorithms is a major problem in compressed sensing. In this talk, I start with a method we developed
based on the analysis of message passing to characterize the phase transition curve for a large class of recovery algorithms. I will then describe the situations in which our analysis fails and propose a method to address such situations. In the end, if time permits, I will also describe several open problems.